Hint: Turn sharply
Press A repeatedly while turning to turn without hitting the forcefield.

Unlock Championship Mode
Not to be confused with the standard Grand Prix Mode, Championship is a hidden option that lets you race a Time Attack challenge against a ghost car on a specialy Synobazz track. The mode also offers the ability to see a replay of the winning run, complete with button commands display. To unlock it, register your name in the rankings of every race in every series.

Get Queen mode
To get queen mode, beat all the expert settings on pawn, knight, and bishop. Now, when you go to the course select, it'll be there.